# Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.2: 21

$\frac{1}{16}$

#### Work Step by Step

When dividing exponential expressions with the same non-zero base, subtract the exponent of the denominator from the exponent of the numerator and give the resulting exponent to the same base: $$\frac{2^{3}}{2^{7}}$$ $$=2^{(3-7)}$$ $$=2^{(-4)}$$ When an exponential expression has a negative exponent, change the position of the base (from the numerator to the denominator, or vise-versa) and make the exponent positive. $$=\frac{1}{2^{4}}$$ $$=\frac{1}{16}$$

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